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VLSI (very large scale integrated) chips incorporate hundreds of millions of semiconductor circuits. To predict the performance of VLSI circuits, the current-voltage (I-V) characteristics of the semiconductor devices are required. Semiconductor device simulation codes provide a way of predicting I-V curves as device parameters are varied, without having to fabricate the device first. Thus, many different designs for devices and circuits can be explored efficiently using computer simulations. Promising designs then can be selected for actual fabrication and testing. A fundamental approach to modeling the quantum transport of electrons and holes in semiconductor devices is the Wigner-Boltzmann equation, the quantum generalization of the Boltzmann equation. Simulating these kinetic equations is computationally expensive. Thus, a hydrodynamic approximation to the kinetic equations, where the density, velocity and temperature of a charge carrier are functions only of three spatial dimensions plus time, offers enormous computational speedups in simulating devices. The article discusses the use of classical and quantum hydrodynamic models in semiconductor device simulation.